ST. LOUIS -- Chris Stewart isn't getting caught up in his own point totals. All the St. Louis Blues power forward cares about is wins.

The Blues are starting to get them -- even with a depleted lineup, they are beginning to catch the fire that led to a 109-point season a year ago.

Stewart continued his torrid pace by scoring two more goals -- he has four in two games -- and adding an assist; Alex Steen scored and added a pair of assists in his return to the lineup; and midseason call-up Jake Allen earned his first NHL shutout when the Blues downed the Phoenix Coyotes 3-0 at Scottrade Center on Thursday night.

Stewart has 12 points (six goals, six assists) in the past six games and 22 points (nine goals, 13 assists) in 17 games. He's supplied more than sufficient offense in the absence of Andy McDonald, T.J. Oshie and Vladimir Tarasenko, all out with injuries for a Blues team that did get Steen back after missing eight games with an upper-body injury.

"I'm not necessarily worried about the points, but I feel like I’m generating a lot of offense," Stewart said. "I'm getting a lot of opportunities on the rush."

Stewart, who had what was considered a down year last season, is generating offense no matter who he's playing with. As recently as a couple games ago, it was with Patrik Berglund and David Perron. Thursday night it was with Steen and David Backes.

"I think confidence with him comes from competing," Blues coach Ken Hitchcock said of Stewart. "He put in all the work in the summer and did a great job, but he's competing. He's competing on every puck, he's not giving up on any pucks, he's not panicking under pressure. He's not thinking he should make another play.

"He's doing a lot of this work himself, but to me, when you're a skill player and you compete at a high level, I don't know many that don't have success, and he has success because of it. He has success because he's determined on the puck. ... He's a very big, strong man that's learning to compete [for] the puck right now. It's very good for us right now."

Allen is 7-1-0 after he stopped 28 shots. He was recalled from the American Hockey League's Peoria Rivermen and stabilized a Blues goaltending situation that looked bleak with a groin injury to Jaroslav Halak and the struggles of Brian Elliott.

"It's something I've dreamed of, especially as a kid getting a shutout in the NHL," said Allen, a second-round pick in the 2008 NHL Draft. "I never would have realized it would have been this quick, but I definitely appreciate all the work the guys did. It's something I won't forget.

"It's sort of a whirlwind the last month or so, whatever it's been. I'm still taking it in stride. I'm really pleased with the way I've played. I couldn't have asked for a better start, but I try to stay even-keeled, stay ready for the next game on Saturday. Just take things one day at a time."

The Coyotes, who had a two-game winning streak stopped, got 27 saves from Mike Smith.

"We came out and took penalty after penalty in the first period," Coyotes coach Dave Tippett said. "You give a home team like that momentum and give them the lead, they’re going to take it and run with it and that’s exactly what they did."

Smith said, "In reality, we didn’t play well enough to win. We didn’t play well enough to get those bounces going our way. We weren’t ready to play from the drop of the puck.

"We had a better second [period] and we obviously were trying to press at the end of the game to get back into it. ... We had a couple of opportunities. As the game wore on, we couldn’t find anything around their net. They got a lead and they held the lead well."

The Blues outshot the Coyotes 16-8 in the first 20 minutes, helped by three power plays, but Smith and Allen were each up to the task.

The Blues' best scoring chances came when fourth-liner Ryan Reaves powered his way to the net and had two point-blank chances thwarted by Smith.

Allen, who obviously didn't see as large a workload, denied Antoine Vermette, who found himself alone at the top of the crease but had a couple whacks at the puck while Allen kept the right pad down. The puck eventually found its way into the net but officials whistled the play dead, saying the puck was covered by Allen when the whistle blew.

Stewart broke the stalemate when a fortuitous bounce wound up on his stick from the other side of the net. Backes' original shot from the left circle caromed off the skate of Phoenix defenseman Derek Morris and off the back boards around the right side of the goal. Stewart was driving the net and skated right onto the puck and slammed it home 5:54 into the second period for a 1-0 Blues lead.

Steen made it 2-0 4:05 into the third period when his initial shot was blocked, but the puck came right back into his wheelhouse in the high slot, and he whirled and fired it past Smith following an odd-man rush for the Blues.

Steen played 19:10 in his return to the ice and he didn't look like he missed a beat.

"That's a lot of credit to my two linemates tonight," Steen said. "Backs and Stew had a heck of a game ... both of them.

"I tried keeping it simple, but both of those two guys, they carried me tonight."

Stewart snapped a shot from the left dot over Smith's glove with plenty of traffic in front with 5:29 remaining as the Blues made it four wins in their past five games.

"This was more of a team shutout. This looked like us. This looked like our team," Hitchcock said. "This looked like [what] we envisioned our team [looking like]. I think there's a collective dig-in going on between the coaches and the players now. I think there's an engagement that's starting to connect now. It's starting to get better and better every day.

"I think people are doing the things that are maybe going unnoticed on the scoreboard. ... The stuff that makes a team is starting to go on in this group now. We're digging in."